73.7.48 problem 48

Internal problem ID [15206]
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
Date solved : Tuesday, January 28, 2025 at 07:49:54 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=x \left (6 y+{\mathrm e}^{x^{2}}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x)=x*(6*y(x)+exp(x^2)),y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{x^{2}}}{4}+{\mathrm e}^{3 x^{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 25

DSolve[D[y[x],x]==x*(6*y[x]+Exp[x^2]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {e^{x^2}}{4}+c_1 e^{3 x^2} \]