Find an explicit solution of the given initial-value problem. x20Y = y - xy, y(-1) = -2 dx y =

Q: Find the particular solution of the differential equation that satisfies the initial conditions.

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Q: Find the exact solution y to the initial-value problem dy/dx= x y^(1/2), y(1) = 4.

A: It is exact solution to the initial value problem.

Q: Find the particular solution of the differential equation that satisfies the initial conditions.

A: The given differential equation is in variable separable form. Hence, an be solved using simple…

Q: , solve the initial value problem.

A: dydx=yln y1+x2

Q: Find an explicit solution of the given initial-value problem. dx dt = 2(x²+1), x( ) = 1 X = Submit…

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Q: Solve the given initial-value problem: dy/dx =(y2 − 1)/(x2 − 1), y(2) = 2

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Q: Find the particular solution of the differential equation yy' – 2e* = 0 that satisfies the initial…

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Q: Solve the given initial-value problem. (x + y)2 dx + (2xy + x² – 4) dy = 0, y(1) = 1

A: This is a question related to differential equation. Based on the general formula and integral…

Q: Find the particular solution of the differential equation y3y′ − 3x = 0 that satisfies the initial…

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Q: Find an explicit solution of the given initial-value problem. x2 dy = y − xy, y(-1) = -3 dx y =

A: We can solve as follows

Q: Find an explicit solution of the given initial-value problem. dx 4(x + 1), x(7/4) = 1 dt

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Q: Solve the given initial-value problems. xe dx + (y-1)dy =0; y(0) =0

A: Differential equation and solution

Q: dy y- 1 dx -1' y(2) = 2

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Q: Find an explicit solution of the given initial-value problem. 1 V1-у? dx - V1-x2 dy — 0, У(0) y =

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Q: Solve the initial value problems d2y/dx2 = sec2 x, y(0) = 0 and y'(0) = 1

A: The given differential equation is: y(0)=0 y’(0)=1

Q: Find the explicit particular solution of the initial value problem given. dy/dx = ye^9x, y(0) = 10e

A: Given. dy/dx = ye9x  => 1/ydy = e9xdx

Q: 5. Find the solution of the differential equation that satisfies the given initial condition. dy =y²…

A: Topic- differential equations

Q: Find an explicit solution of the given initial-value problem. dyy²-1 = y(7) = 7 dx x² y =

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Q: Find an explicit solution of the given initial-value problem. x2 dy=y-xy, y(-1) = -4 dx y =

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Q: Find an implicit and an explicit solution of the initial value problem: y? – 1 dy x2 – 1' y(2) = 2…

A: Given differential equation: dydx=y2-1x2-1 ,  y(2)=2

Q: Solve the initial value problem. dy = 4 e -X, y(0) = 1, y'(0) = 0 2 dx

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Q: Find an explicit solution to the initial value problem: dy = dx y(x) = ex - 5y y(0) = 0

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Q: Find an explicit solution of the given initial-value problem. dx - 3(x² + 1), xG) = 1 dt

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Q: Find an implicit and an explicit solution of the given initial-value problem. dy y – 1 dx x? - 1'…

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Q: Solve the Bernoulli differential equation dy 2 y3 +-y dx X x3

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Q: Find an explicit solution of the given initial-value problem. (1 + x*) dy + x(1 + 4y2) dx = 0, y(1)…

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Q: Find the explicit solution of the initial value problem (xe^(x)+ ye^(x) - 2)dx+ (xe^x + 3)dy=0,…

A: Here we use the concept of exact differential equation

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = -1/ 1-…

A: The given differential equation,1-y2dx-1-x2dy=0, y0=12

Q: Solve the initial value problem.

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Q: Solve the given initial-value problem. (x + y)* dx + (2xy + x- 7) dy = 0, y(1) = 1

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Q: Find an explicit solution of the given initial-value problem. (1 + x²) dy + x(1 + - 4y²) dx = 0,…

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Q: Solve the given initial-value problem. (y2 cos(x) – 3x²y – 4x) dx + (2y sin(x) – x³ + In(y)) dy = 0,…

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Q: Solve the given initial value problem. dy + dx 1 3 xy-3, y(1) = 0 4x

A: Use substitution y^4=v and find integrating factor

Q: Find an explicit solution to the initial value problem dy/dx = 2xy +3y, y(0) = -2

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Q: Find an explicit solution of the given initial-value problem. +²dy x=y=xy, y(-1) = -4 dx y =

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Q: Find an explicit solution of the given initial-value problem. 1 y(4) = 4 y = dy dx = y² x² - - 1

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Q: Find an explicit solution of the given initial-value problem. %3D у — ху, у(-1) %3D —5 dx y = 5C

A: Given differential equation is x2dydx=y−xy ⇒x2dydx=y1−x⇒dyy=1−xx2dx⇒dyy=1x2−xx2dx⇒dyy=1x2−1xdx…

Q: 2. Solve the given initial-value problem. (Exact Equation) (x + y)² dx + (2xy + x² – 1) dy = 0, y(1)…

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Q: Solve the initial value problem. dy + 4y – e-* = 0, dx y(0) = 0 4.

A: GIVEN: dydx + 4y - e-x = 0, y(0) = 0

Q: Find an explicit solution of the given initial-value problem. 1 √1-y² dx √1-x² dy = 0, y(0) = = y =

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Q: Find the solution of the differential equation that satisfies the given initial condition. x +…

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Q: Find an explicit solution of the given initial-value problem. dx = = 6(x² +1), x(1) = = 1 dt x = tan…

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Q: Find an explicit solution of the given initial-value problem. dy/dx = y2-1/x2-1 , y(8) = 8

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Q: y)2

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Q: Find an explicit solution of the given initial-value problem. x2 * (dy/dx) = y - xy, y(-1) = -5

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Q: Solve the given separable initial value problems 1)dy/dx=-2     y=3 when x=0

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Q: 3. Find the solution of the given initial value problem. dy y = xe", y(1) = e – 1, x > 1 | dx

A: I am attaching the solution of question (3) only.  The solution is, y = x(ex - 1)  The detailed…

Q: Find the solution of the differential equation (In(y))³ dy = x'y dx which satisfies the initial…

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Q: Find an explicit solution of the given initial-value problem. dx/dt = 7(x2 + 1),    x x(?/4) = 1

A: Given an initial value problem : dxdt=7x2+1 Also x(4)=1 We need to find an explicit solution. Let's…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.