Differential Equations Answers

1. [(e/√x ^-2√x) - y/√x] = dy/dx
2. xdy/dx +y=x³y⁶
3. dr/dx = tyanchya - r²/coax
4. y dx/dy = x-yx²siny

1. (x²-4xy-2y²)dx + (y²-4xy-2x²)dy=0
2. (x²-xtan²y+sec²y)dy = (tany-2xy-y)dx
3. (2xy⁴e^y+2xy³+y)dx + (x²y⁴e^y-x²y²-3x)dy=0
4. (y/x secy-tany)dx+(secy logx-x)dy=0
5. y dy/dx +4x/3 -y²/3x =0

(D² - 4) y= xe² , xe^x is y_p = (ax + b) e^x

Three students were given a differential equation y''+π ^2y=0 to solve. 

(D² - 4 ) y = xe^x

Reduce to canonical form

u_xx - u_xy + u_yy + u_x = 0

Reduce to canonical form :

𝑢𝑥𝑥 − 𝑢𝑥𝑦 + 𝑢𝑦𝑦 + 𝑢𝑥 = 0

Find the Laplace Transform of half-wave and full-wave

rectified sine wave given in the following figures.

Take w = 2

Find the Laplace Transform of half-wave and full-wave

rectified sine wave given in the following figures.

Take w = 2

Can't we do the Particular solution by assuming sin(z) as imaginery part of e^iz,plz can u show how to do by that method