60.1.361 problem 362

Internal problem ID [10375]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 362
Date solved : Monday, January 27, 2025 at 07:37:26 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} \left (x^{2} y \sin \left (y x \right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (y x \right )-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.276 (sec). Leaf size: 22

dsolve((x^2*y(x)*sin(x*y(x))-4*x)*diff(y(x),x)+x*y(x)^2*sin(x*y(x))-y(x) = 0,y(x), singsol=all)
 

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z} -{\mathrm e}^{-\frac {\cos \left (\textit {\_Z} \right )}{4}} c_{1} x^{{3}/{4}}\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.302 (sec). Leaf size: 79

DSolve[-y[x] + x*Sin[x*y[x]]*y[x]^2 + (-4*x + x^2*Sin[x*y[x]]*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x\left (\sin (K[1] y(x)) y(x)-\frac {1}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (x \sin (x K[2])-\int _1^x(\cos (K[1] K[2]) K[1] K[2]+\sin (K[1] K[2]))dK[1]-\frac {4}{K[2]}\right )dK[2]=c_1,y(x)\right ] \]