20.28 problem 667

Internal problem ID [15432]

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: 667.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {4 x y^{\prime \prime }+2 y^{\prime }+y=1} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 1] \end {align*}

✗ Solution by Maple

dsolve([4*x*diff(y(x),x$2)+2*diff(y(x),x)+y(x)=1,y(infinity) = 1],y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 25

DSolve[{4*x*y''[x]+2*y'[x]+y[x]==1,{y[Infinity]==1}},y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to c_1 \cos \left (\sqrt {x}\right )+c_2 \sin \left (\sqrt {x}\right )+1 \]