69.1.73 problem 117

Internal problem ID [14226]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 117
Date solved : Tuesday, January 28, 2025 at 06:22:36 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]

\begin{align*} y^{\prime \prime }&=\frac {1}{2 y^{\prime }} \end{align*}

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)=1/(2*diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y &= \frac {\left (2 c_{1} +2 x \right ) \sqrt {x +c_{1}}}{3}+c_{2} \\ y &= \frac {\left (-2 c_{1} -2 x \right ) \sqrt {x +c_{1}}}{3}+c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 43

DSolve[D[y[x],{x,2}]==1/(2*D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_2-\frac {2}{3} (x+2 c_1){}^{3/2} \\ y(x)\to \frac {2}{3} (x+2 c_1){}^{3/2}+c_2 \\ \end{align*}