Internal problem ID [13468]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 24. Variation of parameters. Additional exercises page 444
Problem number: 24.1 (L).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }-4 x^{3} y=x^{3} {\mathrm e}^{x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x*diff(y(x),x$2)-diff(y(x),x)-4*x^3*y(x)=x^3*exp(x^2),y(x), singsol=all)
\[ y = \sinh \left (x^{2}\right ) c_{2} +c_{1} \cosh \left (x^{2}\right )+\frac {x^{2} {\mathrm e}^{x^{2}}}{8} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 47
DSolve[x*y''[x]-y'[x]-4*x^3*y[x]==x^3*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{16} \left (\left (2 x^2-1+16 c_1\right ) \cosh \left (x^2\right )+\sinh \left (x^2\right ) \left (\log \left (e^{2 x^2}\right )-1+16 i c_2\right )\right ) \]