Internal problem ID [13159]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.2 (a).
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y^{\prime \prime }-4 x \sqrt {y^{\prime }}=0} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 51
dsolve(diff(y(x),x$2)=4*x*sqrt(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} y \left (x \right ) = \frac {x^{5}}{5}-\frac {2 x^{3}}{3 c_{1}}+\frac {x}{c_{1}^{2}}+c_{2} y \left (x \right ) = \frac {x^{5}}{5}+\frac {2 x^{3}}{3 c_{1}}+\frac {x}{c_{1}^{2}}+c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.095 (sec). Leaf size: 33
DSolve[y''[x]==4*x*Sqrt[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^5}{5}+\frac {c_1 x^3}{3}+\frac {c_1{}^2 x}{4}+c_2 \]