Internal problem ID [9808]
Internal file name [OUTPUT/8751_Monday_June_06_2022_05_23_38_AM_7635885/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1482.
ODE order: 3.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_3rd_order, _linear, _nonhomogeneous]]
Unable to solve or complete the solution.
\[ \boxed {2 x y^{\prime \prime \prime }+3 y^{\prime \prime }+y a x=b} \] Unable to solve this ODE.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & 2 x \left (\frac {d}{d x}y^{\prime \prime }\right )+3 \frac {d}{d x}y^{\prime }+y a x =b \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 3 \\ {} & {} & \frac {d}{d x}y^{\prime \prime } \end {array} \]
Maple trace
`Methods for third order ODEs: --- Trying classification methods --- trying a quadrature trying high order exact linear fully integrable trying differential order: 3; linear nonhomogeneous with symmetry [0,1] trying high order linear exact nonhomogeneous trying differential order: 3; missing the dependent variable checking if the LODE is of Euler type trying Louvillian solutions for 3rd order ODEs, imprimitive case -> pFq: Equivalence to the 3F2 or one of its 3 confluent cases under a power @ Moebius <- pFq successful: received ODE is equivalent to the 0F2 ODE, case c = 0 `
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 1616
dsolve(2*x*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+y(x)*a*x-b=0,y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 14.362 (sec). Leaf size: 2455
DSolve[-b + a*x*y[x] + 3*y''[x] + 2*x*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Too large to display