Internal problem ID [12951]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 2. Integration and differential equations. Additional exercises. page
32
Problem number: 2.4 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime } x=\sqrt {x}-2} \] With initial conditions \begin {align*} [y \left (1\right ) = 8, y^{\prime }\left (1\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve([x*diff(y(x),x$2)+2=sqrt(x),y(1) = 8, D(y)(1) = 6],y(x), singsol=all)
\[ y = \frac {4 x^{\frac {3}{2}}}{3}-2 \ln \left (x \right ) x +6 x +\frac {2}{3} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 26
DSolve[{x*y''[x]+2==Sqrt[x],{y[1]==8,y'[1]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2}{3} \left (2 x^{3/2}+9 x-3 x \log (x)+1\right ) \]