Internal problem ID [13150]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 48.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-x \left (6 y+{\mathrm e}^{x^{2}}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)=x*(6*y(x)+exp(x^2)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x^{2}}}{4}+{\mathrm e}^{3 x^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 25
DSolve[y'[x]==x*(6*y[x]+Exp[x^2]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {e^{x^2}}{4}+c_1 e^{3 x^2} \]