15.6.18 problem 18

Internal problem ID [2975]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 18
Date solved : Monday, January 27, 2025 at 07:05:10 AM
CAS classification : [_linear]

\begin{align*} y x^{\prime }&=2 y \,{\mathrm e}^{3 y}+x \left (3 y +2\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(y*diff(x(y),y)=2*y*exp(3*y)+x(y)*(3*y+2),x(y), singsol=all)
 

\[ x \left (y \right ) = \left (c_{1} y -2\right ) y \,{\mathrm e}^{3 y} \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 18

DSolve[y*D[x[y],y]==2*y*Exp[3*y]+x[y]*(3*y+2),x[y],y,IncludeSingularSolutions -> True]
 

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