Internal problem ID [2016]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-y x -\sqrt {y}\, x \,{\mathrm e}^{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)-x*y(x)=sqrt(y(x))*x*exp(x^2),y(x), singsol=all)
\[ \sqrt {y \left (x \right )}-\frac {{\mathrm e}^{x^{2}}}{3}-{\mathrm e}^{\frac {x^{2}}{4}} c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.307 (sec). Leaf size: 34
DSolve[y'[x]-x*y[x]==Sqrt[y[x]]*x*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{9} e^{\frac {x^2}{2}} \left (e^{\frac {3 x^2}{4}}+3 c_1\right ){}^2 \]