83.31.5 problem 5

Internal problem ID [19397]
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 : 5
Date solved : Tuesday, January 28, 2025 at 01:37:19 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.208 (sec). Leaf size: 20

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

\[ y(x)\to c_2-\frac {\log (a x+c_1)}{a} \]