75.5.20 problem 119

Internal problem ID [16756]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 119
Date solved : Tuesday, January 28, 2025 at 09:21:21 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.285 (sec). Leaf size: 35

dsolve((x+y(x)^3)+3*(y(x)^3-x)*y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \ln \left (x \right )-c_{1} +\frac {\ln \left (\frac {y^{6}+x^{2}}{x^{2}}\right )}{2}-\arctan \left (\frac {y^{3}}{x}\right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.173 (sec). Leaf size: 117

DSolve[(x+y[x]^3)+3*(y[x]^3-x)*y[x]^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\left (\frac {3 \left (K[2]^5-x K[2]^2\right )}{K[2]^6+x^2}-\int _1^x\left (\frac {3 K[2]^2}{K[2]^6+K[1]^2}-\frac {6 K[2]^5 \left (K[2]^3+K[1]\right )}{\left (K[2]^6+K[1]^2\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {y(x)^3+K[1]}{y(x)^6+K[1]^2}dK[1]=c_1,y(x)\right ] \]