Question

.Find the differential equation corresponding y=ae^x+be^2x+ce^3x where a,b,c are arbitrary constant....
Please it's too urgent..... explain step b step........if u give correct answer then mark uu as brainliest...........

Answer 1

Answer:

dy / dx = a(e^x) + 2be^(2x) + 3ce^(3x)

Step-by-step explanation:

Since we given that

y=ae^x+be^2x+ce^3x                where a ,b and c is arbitrary constant

Taking differential on both sides we get

       dy = d(ae^x + be^2x + ce^3x)

Now using the exponential rules of differential and taking constant outside the differential we get

⇒   dy = a(e^x).dx + be^2x . 2dx + ce^3x .3dx

⇒    dy = {a(e^x) + 2be^(2x) + 3ce^(3x)}dx

Dividing by dx on both sides we get

dy / dx = a(e^x) + 2be^(2x) + 3ce^(3x)   ........(1)

Equation (1) is the required differential equation corresponding to given equation.