Internal problem ID [254]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 59.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y=x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x^4,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2} \left (4 \ln \left (x \right ) c_{1} +x^{2}+4 c_{2} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 26
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==x^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x^2 \left (x^2+8 c_2 \log (x)+4 c_1\right ) \]