83.48.15 problem Ex 15 page 110

Internal problem ID [19607]
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 15 page 110
Date solved : Tuesday, January 28, 2025 at 02:04:02 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 19

dsolve(y(x)*(1-ln(y(x)))*diff(y(x),x$2)+(1+ln(y(x)))*diff(y(x),x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.640 (sec). Leaf size: 34

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

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