Internal problem ID [13198]
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: 13.8 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y^{\prime \prime }+2 x {y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)=-2*x*diff(y(x),x)^2,y(0) = 3, D(y)(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = 2 \arctan \left (2 x \right )+3 \]
✓ Solution by Mathematica
Time used: 0.981 (sec). Leaf size: 13
DSolve[{y''[x]==-2*x*y'[x]^2,{y[0]==3,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 \arctan (2 x)+3 \]