83.30.9 problem 9

Internal problem ID [19388]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (D) at page 109
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 01:37:07 PM
CAS classification : [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.269 (sec). Leaf size: 17

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

\[ y(x)\to \log \left (x^2+2 c_1\right )+c_2 \]