Question

Q. Choose the correct answer.
Q. Which of the following is the solution of differential equation du/dx=x^2/(1-u^2 )
i) x3+u3-3u=2
ii) 3/2x3+3/2u3-9/2u=3

iii) -2x3-2u3+6u=4
a. i) only
b. ii) only
c. iii) only
d. i), ii) amd iii)

Answer 1

d)  i), ii) amd iii)

Let's differentiate each of given implicit functions

I)

$$3x^2+3u^2\frac{du}{dx}-3\frac{du}{dx}=0$$

dividing by 3 and separating u and x will give us

$$x^2=\frac{du}{dx}(1-u^2)$$

$$\frac{du}{dx}=\frac{x^2}{1-u^2}$$

which is the given equation

II)

$$\frac{9}{2}x^2+\frac{9}{2}u^2\frac{du}{dx}-\frac{9}{2}\frac{du}{dx}=0$$

dividing by 9/2 and separating u and x will give us

$$x^2=\frac{du}{dx}(1-u^2)$$ $$\frac{du}{dx}=\frac{x^2}{1-u^2}$$

which is the given equation

III)

$$-6x^2-6u^2\frac{du}{dx}+6\frac{du}{dx}=0$$

dividing by 6 and separating u and x will give us

$$x^2=\frac{du}{dx}(1-u^2)$$

$$\frac{du}{dx}=\frac{x^2}{1-u^2}$$

which is the given equation.