83.31.3 problem 3

Internal problem ID [19395]
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 (E) at page 112
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:37:16 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.053 (sec). Leaf size: 20

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {-1+{\mathrm e}^{\left (c_{2} +x \right ) c_{1}}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.495 (sec). Leaf size: 29

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

\begin{align*} y(x)\to \frac {-1+e^{c_1 (x+c_2)}}{c_1} \\ y(x)\to x+c_2 \\ \end{align*}