Internal problem ID [1140]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page
253
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y-x^{2}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
With initial conditions \begin {align*} \left [y \relax (1) = {\frac {5}{4}}, y^{\prime }\relax (1) = {\frac {3}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 11
dsolve([x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-2*y(x) = x^2, x, y(1) = 5/4, D(y)(1) = 3/2],y(x), singsol=all)
\[ y \relax (x ) = x +\frac {1}{4} x^{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 13
DSolve[x^2*y''[x]+2*x*y'[x]-2*y[x]==x^2,{y[1]==5/4,y'[1]==3/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} x (x+4) \\ \end{align*}