Internal problem ID [2256]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 25, page 112
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = x^{2} \left (c_{2} +\ln \left (x \right ) c_{1} +x \right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 19
DSolve[x^2*y''[x]-3*x*y'[x]+4*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2 (x+2 c_2 \log (x)+c_1) \]