7.10.44 problem 51

Internal problem ID [314]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 51
Date solved : Wednesday, February 05, 2025 at 03:18:28 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} a \,x^{3} y^{\prime \prime \prime }+b \,x^{2} y^{\prime \prime }+c x y^{\prime }+d y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 1288

dsolve(a*x^3*diff(y(x),x$3)+b*x^2*diff(y(x),x$2)+c*x*diff(y(x),x)+d*y(x)=0,y(x), singsol=all)
 

\[ \text {Expression too large to display} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 144

DSolve[a*x^3*D[y[x],{x,3}]+b*x^2*D[y[x],{x,2}]+c*x*D[y[x],x]+d*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x^{\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \left (\frac {b}{a}-3\right )+\text {$\#$1} \left (-\frac {b}{a}+\frac {c}{a}+2\right )+\frac {d}{a}\&,1\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \left (\frac {b}{a}-3\right )+\text {$\#$1} \left (-\frac {b}{a}+\frac {c}{a}+2\right )+\frac {d}{a}\&,2\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \left (\frac {b}{a}-3\right )+\text {$\#$1} \left (-\frac {b}{a}+\frac {c}{a}+2\right )+\frac {d}{a}\&,3\right ]} \]