Internal problem ID [6856]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing.
EXERCISES Page 324
Problem number: 39.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }=-x^{2}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}, y^{\prime }\left (0\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.391 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)^2-2*diff(y(x),x$2)+diff(y(x),x)^2-2*x*diff(y(x),x)+x^2=0,y(0) = 1/2, D(y)(0) = 1],y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (x +1\right )^{2}}{2} \\ y \left (x \right ) &= \frac {x^{2}}{2}+\sin \left (x \right )+\frac {1}{2} \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(y''[x])^2-2*y''[x]+(y'[x])^2-2*x*y'[x]+x^2==0,{y[0]==1/2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
Not solved