Internal problem ID [2012]
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: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{3} y^{\prime }+x y^{4}=x \,{\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 114
dsolve(y(x)^3*diff(y(x),x)+x*y(x)^4=x*exp(-x^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= {\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} \\ y \left (x \right ) &= -{\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} \\ y \left (x \right ) &= -i {\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} \\ y \left (x \right ) &= i {\mathrm e}^{-x^{2}} {\left (\left (2 \,{\mathrm e}^{x^{2}}+c_{1} \right ) {\mathrm e}^{2 x^{2}}\right )}^{\frac {1}{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.388 (sec). Leaf size: 200
DSolve[y[x]^3*y'[x]+x*y[x]^4==x*exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{-\frac {x^2}{2}} \sqrt [4]{4 \int _1^xe^{2 K[1]^2} \exp \left (-K[1]^2\right ) K[1]dK[1]+c_1} \\ y(x)\to -i e^{-\frac {x^2}{2}} \sqrt [4]{4 \int _1^xe^{2 K[1]^2} \exp \left (-K[1]^2\right ) K[1]dK[1]+c_1} \\ y(x)\to i e^{-\frac {x^2}{2}} \sqrt [4]{4 \int _1^xe^{2 K[1]^2} \exp \left (-K[1]^2\right ) K[1]dK[1]+c_1} \\ y(x)\to e^{-\frac {x^2}{2}} \sqrt [4]{4 \int _1^xe^{2 K[1]^2} \exp \left (-K[1]^2\right ) K[1]dK[1]+c_1} \\ \end{align*}