66.2.1 problem Problem 1

Internal problem ID [13900]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 1
Date solved : Tuesday, January 28, 2025 at 06:07:58 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+10 y&=100 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=10\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)-6*diff(y(x),x)+10*y(x)=100,y(0) = 10, D(y)(0) = 5],y(x), singsol=all)
 

\[ y = 5 \sin \left (x \right ) {\mathrm e}^{3 x}+10 \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 17

DSolve[{D[y[x],{x,2}]-6*D[y[x],x]+10*y[x]==100,{y[0]==10,Derivative[1][y][0] ==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 \left (e^{3 x} \sin (x)+2\right ) \]