I need a help to solve these ODE problms
Test for exactness. If exact, solve. If not, use an integrating factor to reduce to exact and solve.
Q1)
y1 = x3/2 and y2 = x-1/2 are solutions of the ODE 4x2 y? - 3y = 0. Solve the IVP subject to: y(1) = -3 and y?(1) = 0.
Q2)
The ODE y y = 3y?2 can be reduced to a first-order ODE with y as the independent variable, z = y?, and y? = (dz/dy)z. Reduce to first order and solve
Wolfram|Alpha Pro can distinguish whether an ODE is exact or not. Additionally, it can show the steps you’d take to solve the equation using that knowledge. For example:
http://www.wolframalpha.com/input/?i=2+x+y±+9+x%5E2+%2B+%282+y+%2B+x%5E2+%2B1%29+dy%2Fdx+%3D%3D0
If you’d like help with specific problems and learning how to solve ODEs by hand, using Wolfram|Alpha Pro is probably the best way to do this.
There are some good tutorials available for solving exact ODEs such as: