60.1.355 problem 356

Internal problem ID [10369]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 356
Date solved : Monday, January 27, 2025 at 07:33:43 PM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 19

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

\[ y^{2} \sin \left (x \right )+x^{2} \sin \left (y\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 76

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

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