SOLUTION: Reduce the given cauchy-Euler equation to a linear differential equation with constant coefficient. X^2.d^2y/dx^2 -2Xdy/dx+2y=X^3. ? (8 marks)

Question 1025056: Reduce the given cauchy-Euler equation to a linear differential equation with constant coefficient.
X^2.d^2y/dx^2 -2Xdy/dx+2y=X^3. ? (8 marks)

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

Use the transformation
==> ==>
==>
==>
==>
==>
==> <--Equation (A)
Now try the particular solution
By substitution into Equation (A), we get C = 1/2.
==> the general solution to Equation (A) is
<-- Equation (B)
==> Now from and by direct substitution into Equation (B), we get
,
the general solution to the original Cauchy-Euler equation.

RELATED QUESTIONS
d the specific solution of the differential equation dy/dx= 2y/x^2 with condition... (answered by Edwin McCravy)

Please help me with this problem: Find a general solution to the differential equation... (answered by Boreal)

Find the general solution of this linear differential equation: (x^4... (answered by Edwin McCravy)

Find a general solution of the differential equation: d^(4)y/dx^(2) -4 d^(3)y/dx^(3)... (answered by fractalier)

Find the particular integral for the differential equation X^2 d^2 /dx^2 -X dy/dx... (answered by robertb)

{{{(x^2 + 2) d^2y/dx^2 + 3x dy/dx - y = 0}}} (tried to write this as simply (x^2 +... (answered by Edwin McCravy)

please any one solve this differential equation :... (answered by Edwin McCravy)

Solve the differential equation (x^2 - 8x + 15) dy/dx = 6y +... (answered by Edwin McCravy)

how can i identify a linear equation... by seeing the equation. . and cant... (answered by rfer)