82.40.6 problem Ex. 6

Internal problem ID [18952]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 94
Problem number : Ex. 6
Date solved : Tuesday, January 28, 2025 at 12:38:14 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]]

\begin{align*} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }&=x y^{2} \end{align*}

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved