15.7.6 problem 6

Internal problem ID [2987]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 6
Date solved : Monday, January 27, 2025 at 07:05:48 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ \sqrt {y}-\frac {{\mathrm e}^{x^{2}}}{3}-{\mathrm e}^{\frac {x^{2}}{4}} c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.334 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{9} e^{\frac {x^2}{2}} \left (e^{\frac {3 x^2}{4}}+3 c_1\right ){}^2 \]