Internal problem ID [1123]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y=4 x^{2}} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve([x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+8*y(x)=4*x^2,x^2],y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x^{4}+c_{1} x^{2}+x^{2} \left (-1-2 \ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 23
DSolve[x^2*y''[x]-5*x*y'[x]+8*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 \left (c_2 x^2-2 \log (x)-1+c_1\right ) \]