Question

1. Find the general solution of the following differential equation 4xdx - 3ydy = 3x^2ydy - 2xy^2dx. 2. Solve the Cauchy problem (Use Lagrange/ Bernoulli Method) y' - y/x = x sin x , y(?/2) = 1. 3. Find the general solution of the differential equation. (e^y cos x - y^2 sin x)dx + (e^y sin x + 2y cos x)dy = 0 4. Find the general solution of the following differential equation using reduction of order method x^2y'' = y'^2.

          1. Find the general solution of the following differential equation
4xdx - 3ydy = 3x^2ydy - 2xy^2dx.
2. Solve the Cauchy problem (Use Lagrange/ Bernoulli Method)
y' - y/x = x sin x , y(?/2) = 1.
3. Find the general solution of the differential equation.
(e^y cos x - y^2 sin x)dx + (e^y sin x + 2y cos x)dy = 0
4. Find the general solution of the following differential equation using reduction of order method
x^2y'' = y'^2.

1. Find the general solution of the following differential equation
4xdx - 3ydy = 3x^2ydy - 2xy^2dx.
2. Solve the Cauchy problem (Use Lagrange/ Bernoulli Method)
y' - y/x = x sin x , y(?/2) = 1.
3. Find the general solution of the differential equation.
(e^y cos x - y^2 sin x)dx + (e^y sin x + 2y cos x)dy = 0
4. Find the general solution of the following differential equation using reduction of order method
x^2y” = y'^2.

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Differential Equations

Shepley L. Ross 3rd Edition

Chapter 4

Instant Answer

Solved by Expert Khoi V

05/07/2024

Step 1

The given differential equation can be rewritten as: \[ 4x dx - 3y dy = 3x^2y dy - 2xy^2 dx \] Rearranging terms, we get: \[ 4x dx + 2xy^2 dx = 3y dy + 3x^2y dy \] Factoring out common terms, we get: \[ 2x(2 dx + xy^2 dx) = 3y( dy + x^2y dy) \] Dividing both sides Show more…

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