Find the solution of the differential equation that satisfies the given initial condition. dL = kL² In(t), L(1) = -10 dt

Q: Solve the given differential equation with initial condition. 7y= 2y', y(0) = 7

A: As the solution statement shows that y is the function of t. So we will proceed accordingly.

Q: Find the solution of the differential equation that satisfies the given initial condition. xy' + y =…

A: The given differential equation is  xy' + y = y2, y(1) = - 10

Q: Find the general solution of the differential equation.

A:

Q: Find the solution r(t) of the differential equation with the given initial condition:

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Q: Find the general solution of the second order differential equation below: dx d) dt2 + 6x = 0 dt

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Q: Find the general solution of the differential equation 2 = -5(y – 3). dy %D dt

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Q: dy dx

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Q: Find the solution of the differential equation that satisfies the given initial condition. dp/dt =…

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Q: Solve the given differential equation with initial condition.  y' = 4y, y(0) = 0

A: We rewrite the differential equation as dydx=4y. Now dy4y=dx⇒∫dy4y=∫dx⇒14∫dyy=∫dx⇒14 ln y=x+C1⇒ln…

Q: Solve the given differential equation by separation of variables. dP = p - p² dt P ||

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Q: Find the general solution of the first-order linear differential equation. xy' + y = x³3 + 1

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

A: Consider the given differential equation,

Q: Find particular solution to the differential equation, given initial conditions f" (x) = 5x² + 6x,…

A:

Q: Solve the given differential equation with initial condition.  y' = 3y, y(0) = 1

A: Given: y' = 3y,  y(0) = 1 To solve: The given differential equation with the given initial…

Q: Find the general solution of the given second-order differential equation. у" - у' — 20у %3D 0 y(x)…

A: Given that: y''-y'-20y=0

Q: Solve the given differential equation with initial condition. 5y = 3y', y(0) = 7

A: Given: 5y=3y',     y0=7 We can write it as, 5y=3dydx⇒1ydy=53dx Integrate on both sides we get,…

Q: dy 3x + 2y y(- dx 3x+ 2γ +2 '

A:

Q: The solution of the separable differential equation = (1+y²)x is: %3D dx

A:

Q: Solve the differential equation. dz/dt + et + z = 0

A: Given : dzdt+et+z=0

Q: x In x = y(1 + 3 + y² ) y', y(1) = 1 %3D

A: Let us consider the differential equation of the form dydx=f(x)g(y) Then to solve the equation using…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =…

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Q: Find the general solution of the differential equation: 3ydx = (3x + 1)dy

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Q: Verify that the indicated expression is an implicit solution of the given first-order differential…

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Q: Solve the given differential equation with initial condition.  y' = 2y, y(0) = 2

A: given,             y'=2y       and y(0) = 2

Q: Solve the given differential equation with initial condition.  y' = y, y(0) = 4

A: Given : y' = yy0 = 4

Q: Find the solution of the differential equation that satisfies the given initial conc (x)uj x = y1 +…

A: Solution :-

Q: Solve differential equation, subject to the given initial condition.

A: Given,

Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: Given information: The differential equation is dPdt=Pt. Calculation: Solve the given differential…

Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =…

A:

Q: The solution of the differential equation + 2y = a is, Oy = +c Oy= Oy = Oy= T

A: The objective is to find the solution of the differential equation.

Q: Find the solution to the differential equation x y y' = 2 satisfying the initial condition y(e) = 4.

A: To solve the following problem by seperation of variable and using the boundery condition to find…

Q: A particular solution of the differential equation y" – 2y' + y = e* is

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Q: y= c, e2t + Cze-+

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Q: Consider the autonomous differential equation, without solving, sketch what the solution curve would…

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Q: Find the general solution of the first-order linear differential equation. +3y=6 dx

A: Let the given differential equation is: dydx+Py=Q where P and Q are functions of x (or constants)…

Q: Find the solution of the differential equation that satisfies the given initial condition. dP 5V Pt,…

A: Given query is to solve the initial condition differential equation.

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

A: Given,  f'(x)=6x, f(0)=7

Q: Solve the differential equation

A:

Q: Solve the given differential equation by separation of variables. dP = p-p² dt

A: The given differential equation is: dPdt=P-P2 We have to solve the given differential equation using…

Q: (x-1) dy + (y-2) dx = 0

A: To solve the given differential equation

Q: Solve the initial value problem of first order linear differential equation: x+y=e*; y(1) = 2.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the general solution to the differential equation. dx 130 dt : = 3r° (x² + 4) -

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

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

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

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Q: 2(2x? + у?)dx — ху dy %3D 0

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Q: dx (1+1)-+x=t. dt

A: The differential equation is given as (t+1)dxdt+x=t It can be rewritten as dxdt+xt+1 = tt+1 It is a…

Q: Consider the differential equation: 1 y"- 3y' + 2y = 1+e* What is the general solution?

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Q: Find the general solution of the given second-order differential equation. бу" + у' %3D 0 y(x) =

A:

Q: Solve the given differential equation by separation of variables. dp = p-p² dt

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.