67.3.25 problem Problem 26

Internal problem ID [14043]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 26
Date solved : Tuesday, January 28, 2025 at 06:13:09 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+10 y^{\prime }&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 8.770 (sec). Leaf size: 11

dsolve([diff(y(t),t$3)-6*diff(y(t),t$2)+10*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 3, (D@@2)(y)(0) = 8],y(t), singsol=all)
 

\[ y = {\mathrm e}^{3 t} \cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 60.047 (sec). Leaf size: 59

DSolve[{D[ y[t],{t,3}]-6*D[y[t],{t,2}]+10*D[y[t],t]==0,{y[0]==1,Derivative[1][y][0] ==3,Derivative[2][y][0] ==8}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^te^{3 K[1]} (3 \cos (K[1])-\sin (K[1]))dK[1]-\int _1^0e^{3 K[1]} (3 \cos (K[1])-\sin (K[1]))dK[1]+1 \]