15.10.19 problem 19

Internal problem ID [3106]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 18, page 82
Problem number : 19
Date solved : Monday, January 27, 2025 at 07:19:30 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }-3 y^{\prime \prime }+10 y^{\prime }-15 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

dsolve(2*diff(y(x),x$3)-3*diff(y(x),x$2)+10*diff(y(x),x)-15*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {3 x}{2}}+c_2 \sin \left (\sqrt {5}\, x \right )+c_3 \cos \left (\sqrt {5}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 38

DSolve[2*D[y[x],{x,3}]-3*D[y[x],{x,2}]+10*D[y[x],x]-15*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^{3 x/2}+c_1 \cos \left (\sqrt {5} x\right )+c_2 \sin \left (\sqrt {5} x\right ) \]