Internal problem ID [12498]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 126.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]
\[ \boxed {y^{\prime \prime }-\frac {1}{2 y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)=1/(2*diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (2 x +2 c_{1} \right ) \sqrt {c_{1} +x}}{3}+c_{2} \\ y \left (x \right ) &= \frac {\left (-2 x -2 c_{1} \right ) \sqrt {c_{1} +x}}{3}+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 43
DSolve[y''[x]==1/(2*y'[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*}