75.20.28 problem 667

Internal problem ID [17162]
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 ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 667
Date solved : Tuesday, January 28, 2025 at 09:54:51 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x y^{\prime \prime }+2 y^{\prime }+y&=1 \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.918 (sec). Leaf size: 5

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

\[ y = 1 \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

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

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