Internal problem ID [8650]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 314.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{3} y^{\prime } x +y^{4}=x \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 170
dsolve(x*y(x)^3*diff(y(x),x)+y(x)^4-x*sin(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\left (-4 \cos \left (x \right ) x^{4}+16 \sin \left (x \right ) x^{3}+48 \cos \left (x \right ) x^{2}-96 \cos \left (x \right )-96 x \sin \left (x \right )+c_{1} \right )^{\frac {1}{4}}}{x} y \left (x \right ) = -\frac {\left (-4 \cos \left (x \right ) x^{4}+16 \sin \left (x \right ) x^{3}+48 \cos \left (x \right ) x^{2}-96 \cos \left (x \right )-96 x \sin \left (x \right )+c_{1} \right )^{\frac {1}{4}}}{x} y \left (x \right ) = -\frac {i \left (-4 \cos \left (x \right ) x^{4}+16 \sin \left (x \right ) x^{3}+48 \cos \left (x \right ) x^{2}-96 \cos \left (x \right )-96 x \sin \left (x \right )+c_{1} \right )^{\frac {1}{4}}}{x} y \left (x \right ) = \frac {i \left (-4 \cos \left (x \right ) x^{4}+16 \sin \left (x \right ) x^{3}+48 \cos \left (x \right ) x^{2}-96 \cos \left (x \right )-96 x \sin \left (x \right )+c_{1} \right )^{\frac {1}{4}}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.637 (sec). Leaf size: 164
DSolve[-(x*Sin[x]) + y[x]^4 + x*y[x]^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [4]{16 x \left (x^2-6\right ) \sin (x)-4 \left (x^4-12 x^2+24\right ) \cos (x)+c_1}}{x} y(x)\to -\frac {i \sqrt [4]{16 x \left (x^2-6\right ) \sin (x)-4 \left (x^4-12 x^2+24\right ) \cos (x)+c_1}}{x} y(x)\to \frac {i \sqrt [4]{16 x \left (x^2-6\right ) \sin (x)-4 \left (x^4-12 x^2+24\right ) \cos (x)+c_1}}{x} y(x)\to \frac {\sqrt [4]{16 x \left (x^2-6\right ) \sin (x)-4 \left (x^4-12 x^2+24\right ) \cos (x)+c_1}}{x} \end{align*}