83.48.9 problem Ex 9 page 104

Internal problem ID [19601]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 9 page 104
Date solved : Tuesday, January 28, 2025 at 02:01:22 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved