Name: Formation of Differential Equations
Uploaded: 2019-07-19
Duration: 11 min 9 s
Description: In this video, we are going to learn about the formation of differential equations in detail. Master this concept in just a few minutes with this quick lesson.

Question

Find the differential equation of the curve

y = a e^{3 x} + b e^{5 x}

.

Accepted Answer

Given that, we have the equation of the curve is $y = a e^{3 x} + b e^{5 x} \to (1)$

Since, the given family curve have two arbitrary constants i..e, $a$ and $b$ , so we need to differentiate twice.

Now, differentiate $y$ with respect to $x$ , we get: $\frac{d y}{d x} = 3 a e^{3 x} + 5 b e^{5 x} = 3 (y - b e^{5 x}) + 5 (y - a e^{3 x})$ [Using $(1)$ ]

$= 8 y - (3 b e^{5 x} + 5 a e^{3 x})$

Again differentiate with respect to $x$ , then we get: $\frac{d^{2} y}{d x^{2}} = 8 \frac{d y}{d x} - (15 b e^{5 x} + 15 a e^{3 x})$

$\Rightarrow \frac{d^{2} y}{d x^{2}} = \frac{8 d y}{d x} - 15 y$ [Since, $y = a e^{3 x} + b e^{5 x}$ ]

$\Rightarrow \frac{d^{2} y}{d x^{2}} - \frac{8 d y}{d x} + 15 y = 0$ , which is the required differential equation.

Find the differential equation of the curve $y = a e^{3 x} + b e^{5 x}$ .

Important Questions on Differential Equations

Learn and Prepare for any exam you want !

Find the differential equation of the curve y=ae3x+be5x.

Important Questions on Differential Equations

Learn and Prepare for any exam you want !

Find the differential equation of the curve $y = a e^{3 x} + b e^{5 x}$ .