1. Determine the general solution of the following nonhomogeneous linear equations. dy 1. dx ex 2+ y +y = dx x²+1

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 solution of the following differential equations: Parallel Lines (x – 2y + 3) dx + (3x – 6y…

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Q: 4. Find the solution of the following set of simultaneous equations by LT with conditions y(0) =…

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Q: 1. Find the general solution of: du dx _ _ y + xy² + x³ x+x²y+y² dy

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Q: Solve the the initial value dy problem dt 2t y + t?y Y(0) = -2.

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Q: Find the solution to the initial-value problem. dy = y³xe*, y(0) = 1 dx II

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Q: Use the fact that 5x2 – y? = c is a one-parameter family of solutions of the differential equation y…

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Q: 6. Which of the following differential equationsis not a linear? a. dt ds +2 = 2t° dy c. dx + 3xy =…

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Q: Calculate the solution to the differential equ y (y² + 3x²) dx + 2r*dy = 0 O x³ = y² (C – x) x²C = 3…

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Q: 1. Find the general/particular solution of the following linear equation at first order. a. x²dy -…

A: Given : The following are the three linear equation of 1st order a  x2dy-sin2xdx+3xydx=0b…

Q: Find the solution to the initial value problem: dy = 5y dx y(x) = y(1) = 1

A: Introduction The initial value problem is solved using various techniques. In this question, the…

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: Solve the following linear differential equation system, i.e., find y₂(t). dyn (1) dt dyż (t) dt =…

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Q: 5 dy ay =2ex, y(0)=3 is dx %3D The solution for the initial value problem y =2ex+1 y=2ex+1+c

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Q: dx -8y=0 dx d'y ,d'y d'y dy +35 dx dx' dx dx -0, y(0) =y'(0)=0, y"(0) =y"(0)=1 d)

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Q: 21. dy 2xy = 3y, y(1) = } dx

A: First we convert the given Bernoulli differential equation into linear differential equation, after…

Q: Find the solution of the initial value problem y" + 2y' + 5y = 12e cos(2t), y(0) = 8, y'(0) = 0. %3D…

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Q: 4. Find the solution of the following set of simultaneous equations by LT with initial conditions…

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Q: Find the solution of the initial value problem. dy dx 1+y y(0) =1 %3D

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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 the solution of the initial value problem dy/dx=27e^6x_3y ,y(0)=0

A: This is a problem related to differential equation. Based on the integrating factor formula we will…

Q: 6. What is the general solution of the following differential a²ycdy d²y dx2 dy equation -5 +4y=0)(4…

A: Given differential equations are, d2ydx2-5dydx+4y=04d2ydx2+6dydx+2y=0 Solve the equation by solving…

Q: Find the general solutions of the following differential equations. d²y_2 - 2 + 4y = 0 (a) dx? d'y…

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Q: 1. State the order of the following differential equations. Which are linear and nonlinear? dy d²y…

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Q: 4. Find the solution of the following set of simultaneous equations by LT with initial conditions…

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Q: Solve the following system of linear differential equations: dx/dt =2x+2y+2, dy/dt =x+3y+2

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Q: Find an explicit solution of the given initial-value problem. 2 V1- y? dx - V1- x² dy = 0, y(0) = 2…

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Q: What is the order and the degree of the following differential equations? 3 (d²y` 1. dx² + 3y () +y…

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

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Q: Solve the initial value problem. dy + 9ху%3 8х, у(0)%3D 2 -9xy = y(0) = 2 dx

A: The given differential equation is, The given initial condition is y(0) = 2. Solve the given…

Q: (b) solve the system of differential equations dx dt dy dt + (x + 2y) + 2(x - y) = 1 = = t

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Q: Find the solution of the following differential equations: Parallel Lines (3x – y – 1) dx + (9x – 3y…

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Q: Solve the general or particular solution for the following homogeneous equations. (25x + 3y) dy −…

A: We have to solve the general or particular solution for the following homogeneous equations (25x +…

Q: 4. Find the solution of the following set of simultaneous equations by LT with initial conditions…

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Q: In problems  determine by inspection at least two solutions of the   1. x dy/dx =2y,  y(0)=0

A: Given: xdydx=2y, y0=0 for solving given differential equation we will use variable separable method

Q: Find the general solutions of the following differential equations. d’y dy +42 +9y = 4e* d'y dy а)…

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

Q: Which of the following differential equations is not homogeneous? A (x² – xy)dx – ((²+ xy)dy = 0 B…

A: In this question, we need to check which of the given differential equations is not homogenous. As…

Q: Find the general solutions of the following differential equations. d'y dy +4 +9y = 4e" d'y dy - 3y…

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Q: Obtain the general solution to the equation. (3t + 4y + 2)dt – dy = 0

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Q: Use the method of separable equations to solve the following initial value problems. dx/dt=…

A: It is given that dx/dt=xsin(t) with initial condition x(0) =1 and xy′=y2 with initial condition y(1)…

Q: Solve the given initial value problem. dx = 3x + y- e 3t, x(0) = 1 %3D dt dy = 4x + 3y, dt У(0) - -…

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Q: Find the solution of the following initial-value problem d^2y/dx^2+dy/dx+ 4y = e^x , y(0) = 1,…

A: We have to find solutions

Q: Which of the following differential equations is not linear? option 1: (dy/dx) + xy^2 = e^x option…

A: Solution :- we have to find which of the                            differential equation is not…

Q: 1. Find the general solution of: dx dy _y+xy²+x² x+x²y+y³

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Q: Which of the following differential equations are NOT linear? i) ty'-t^3y=15ty′−t3y=15 ii)…

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Q: Solve the initial-value problem. dy (x² + 1) Y + 3x(y – 1) = 0, y(0) = 7 %3D dx

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