The desolve (or deSolve) command can solve:
deSolve is a synonym for desolve.
In the differential equations, the function y can be denoted by y or y(x), the derivative by y′, y′(x) or diff(y(x),x), etc.
Examples.
e−x | ⎛ ⎝ | c0 x+c1 | ⎞ ⎠ |
e−x | ⎛ ⎝ | x+1 | ⎞ ⎠ |
e−t | ⎛ ⎝ | c0 t+c1 | ⎞ ⎠ |
e−t | ⎛ ⎝ | t+1 | ⎞ ⎠ |
y″+y=cos(x) |
c0 cosx+c1 sinx+ |
|
c0 cost+c1 sint+ |
|
y″+y=cos(x), y(0)=1 |
| cosx+c1 sinx+ |
|
y″+y=cos(x) (y(0))2=1 |
⎡ ⎢ ⎢ ⎣ |
| +c1 sinx+ |
| ,− |
| +c1 sinx+ |
| ⎤ ⎥ ⎥ ⎦ |
y″+y=cos(x), (y(0))2=1 y′(0)=1 |
⎡ ⎢ ⎢ ⎣ |
| +sinx+ |
| ,− |
| +sinx+ |
| ⎤ ⎥ ⎥ ⎦ |
y″+2y′+y=0 |
e−x | ⎛ ⎝ | c0 x+c1 | ⎞ ⎠ |
y″−6y′+9y=xe3x |
e3 x | ⎛ ⎝ | c0 x+c1 | ⎞ ⎠ | + |
| x3 e3 x |
xy′+y−3x2=0 |
|
y′+x*y=0, y(0)=1 |
e |
|
x(x2−1)y′+2y=0 |
|
x(x2−1)y′+2y=x2 |
|
t(t2−1)y′(t)+2y(t)=t2 |
|
x(x2−1)y′+2y=x2,y(2)=0 |
|
√ |
| y′−x−y= | √ |
|
|
y′=2 | √ |
|
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ | ⎛ ⎜ ⎜ ⎝ | − |
| c0+x | ⎞ ⎟ ⎟ ⎠ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
xy′ln(x)−y(3ln(x)+1)=0 |
c0 x3 lnx |
xy′+2y+xy2=0 |
⎡ ⎢ ⎢ ⎣ | 0,− |
| ⎤ ⎥ ⎥ ⎦ |
xy′−2y=xy3 |
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ | ⎛ ⎜ ⎜ ⎝ | ⎛ ⎜ ⎜ ⎝ | − |
| · 2 x5+c0 | ⎞ ⎟ ⎟ ⎠ | e−4 lnx | ⎞ ⎟ ⎟ ⎠ |
| ,− | ⎛ ⎜ ⎜ ⎝ | ⎛ ⎜ ⎜ ⎝ | − |
| · 2 x5+c0 | ⎞ ⎟ ⎟ ⎠ | e−4 lnx | ⎞ ⎟ ⎟ ⎠ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
x2y′−2y=xe(4/x)y3 |
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ | ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ | ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ | − | ∫ | 2 x4 | ⎛ ⎜ ⎝ | e |
| ⎞ ⎟ ⎠ |
| dx+c0 | ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ | e−4 lnx | ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ |
| ,− | ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ | ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ | − | ∫ | 2 x4 | ⎛ ⎜ ⎝ | e |
| ⎞ ⎟ ⎠ |
| dx+c0 | ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ | e−4 lnx | ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
3x3y′=y(3x2−y2) |
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ | 0,− |
| , |
| ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ |
yy′+x=0 |
⎡ ⎢ ⎣ | √ |
| ,− | √ |
| ⎤ ⎥ ⎦ |
2xyy′+x2−y2+a2=0 |
⎡ ⎢ ⎣ | √ |
| ,− | √ |
| ⎤ ⎥ ⎦ |
(y+y′)4+y′+3y=0 |
dy/dt=f′(t)=y′*dx/dt=g(t)*dx/dt |
y=−t−8*t4, y′=dy/dx=3*t+8*t4 dy/dt=−1−32*t3 |
(3*t+8*t4)*dx=(−1−32*t3)dt |
|
x(t)=−11*1/9*ln(8*t3+3)+1/−9*ln(t3)+c0, y(t)=−t−8*t4 |
xy′+y′3−y=0 |
⎡ ⎣ | c0 x+c03 | ⎤ ⎦ |
y−xy′ − | √ |
| =0 |
⎡ ⎢ ⎣ | c0 x+ | √ |
| ⎤ ⎥ ⎦ |