15.5.12 problem 12

Internal problem ID [2948]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:00:14 AM
CAS classification : [_Bernoulli]

\begin{align*} {\mathrm e}^{x} y^{\prime }&=2 x y^{2}+y \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y = \frac {{\mathrm e}^{x}}{-x^{2}+c_1} \]

✓ Solution by Mathematica

Time used: 0.337 (sec). Leaf size: 25

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

\begin{align*} y(x)\to -\frac {e^x}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}