Internal problem ID [13172]
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: 13.4 (a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }-{y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 5, y^{\prime }\left (0\right ) = 15] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 10
dsolve([y(x)*diff(y(x),x$2)=diff(y(x),x)^2,y(0) = 5, D(y)(0) = 15],y(x), singsol=all)
\[ y \left (x \right ) = 5 \,{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 12
DSolve[{y[x]*y''[x]==y'[x]^2,{y[0]==5,y'[0]==15}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 5 e^{3 x} \]