Internal problem ID [15411]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 642.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y=1} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([(1+x^2)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=1,x],singsol=all)
\[ y \left (x \right ) = \sqrt {x^{2}+1}\, c_{2} +c_{1} x -1 \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 80
DSolve[(1+x^2)*y''[x]+x*y'[x]-y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\sqrt {x^2+1}+(c_1-i c_2) x^2+x \left (c_1 \left (-\sqrt {x^2+1}\right )+i c_2 \sqrt {x^2+1}+1\right )+c_1}{\sqrt {x^2+1}-x} \]