## Related questions with answers

Explain the basic concepts ordinary and partial differential equations (ODEs, PDEs), order, general and particular solutions, initial value problems (IVPs). Give examples.

Solution

VerifiedIf the derivatives in the equation are ordinary, the equation is said to be **ordinary (ODE)**.

*Example:*

$y' + y = 0$

$\frac{dy}{dx} + (x+ 15) y = 0$

If the derivatives in the equation have refrence tot two or more independent variables, the equation is said to be **partial (PDE)**.

*Example:*

$x \frac{d^2y}{dx^2} + (2x-1)y \frac{dy}{dx} + xy = 0$

If the $n$th derivative is the highest derivative in the equation, that equation is said to be **of order** '$n$'.

*Example:*

$y''' + 3y'' - 3y' + y = 30e^x$

Order of this differential equation is $3$.

$y^{\text{iv}} + 10 y '' - 9y = 0$

Order of this differential equation is $4$.

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