75.7.11 problem 186

Internal problem ID [16804]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 186
Date solved : Tuesday, January 28, 2025 at 09:31:17 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 24.342 (sec). Leaf size: 5

dsolve([( 2*x/y(x)^3)+( (y(x)^2-3*x^2)/y(x)^4 )*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
 

\[ y = x \]

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 43

DSolve[{( 2*x/y[x]^3)+( (y[x]^2-3*x^2)/y[x]^4 )*D[y[x],x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

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