60.1.313 problem 314

Internal problem ID [10327]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 314
Date solved : Monday, January 27, 2025 at 07:12:26 PM
CAS classification : [_Bernoulli]

\begin{align*} x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 156

dsolve(x*y(x)^3*diff(y(x),x)+y(x)^4-x*sin(x) = 0,y(x), singsol=all)
 

\begin{align*} y &= \frac {{\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_{1} \right )}^{{1}/{4}}}{x} \\ y &= -\frac {{\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_{1} \right )}^{{1}/{4}}}{x} \\ y &= -\frac {i {\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_{1} \right )}^{{1}/{4}}}{x} \\ y &= \frac {i {\left (4 \left (-x^{4}+12 x^{2}-24\right ) \cos \left (x \right )+16 \left (x^{3}-6 x \right ) \sin \left (x \right )+c_{1} \right )}^{{1}/{4}}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.329 (sec). Leaf size: 136

DSolve[-(x*Sin[x]) + y[x]^4 + x*y[x]^3*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\ y(x)\to -\frac {i \sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\ y(x)\to \frac {i \sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\ y(x)\to \frac {\sqrt [4]{4 \int _1^xK[1]^4 \sin (K[1])dK[1]+c_1}}{x} \\ \end{align*}