75.22.10 problem 715

Internal problem ID [17189]
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 17. Boundary value problems. Exercises page 163
Problem number : 715
Date solved : Tuesday, January 28, 2025 at 09:56:38 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y^{\prime }\left (0\right )&=\alpha \\ y^{\prime }\left (\pi \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.127 (sec). Leaf size: 21

dsolve([diff(y(x),x$2)+alpha^2*y(x)=1,D(y)(0) = alpha, D(y)(Pi) = 0],y(x), singsol=all)
 

\[ y = \sin \left (\alpha x \right )+\cos \left (\alpha x \right ) \cot \left (\alpha \pi \right )+\frac {1}{\alpha ^{2}} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],{x,2}]+\[Alpha]^2*D[y[x],x]==1,{Derivative[1][y][0] ==\[Alpha],Derivative[1][y][Pi]==0}},y[x],x,IncludeSingularSolutions -> True]
 

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