MCQOPTIONS
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MCQOPTIONS
This section includes 5 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the general solution of the D.E y = 2xy 3(y )2. |
| A. | (y(p) = p^{1/2} + frac{c}{2p} ) |
| B. | (y(p) = p^2 + frac{2c}{p} ) |
| C. | (x(p) = -cp + frac{c}{p^2} ) |
| D. | (x(p) = 2p + frac{2c}{p^2} ) |
| Answer» C. (x(p) = -cp + frac{c}{p^2} ) | |
| 2. |
Find the general solution of the D.E 2y-4xy -log y =0. |
| A. | (y(p) = frac{2c}{p} 1 + frac{log u2061p}{2} ) |
| B. | (y(p) = frac{c}{2p} 2 + log u2061p ) |
| C. | (x(p) = frac{-1}{p} + frac{c}{p^2} ) |
| D. | (x(p) = frac{1}{2p} + frac{c}{p^{1/2}} ) |
| Answer» B. (y(p) = frac{c}{2p} 2 + log u2061p ) | |
| 3. |
Find the general solution for the equation (px-py)(py+x)=2p by reducing into Clairaut s form by using the substitution X=x2, Y=y2 where p= ( frac{dy}{dx} ). |
| A. | (y^2 = x + frac{c}{c+1} ) |
| B. | (y^2 = cx^2 frac{2c}{c+1} ) |
| C. | (x^2 = cy^2 frac{1}{2c+1} ) |
| D. | (x^2 = y^2 + frac{c}{2c+2} ) |
| Answer» C. (x^2 = cy^2 frac{1}{2c+1} ) | |
| 4. |
Obtain the general solution for the equation xp2+px-py+1-y=0 where p= ( frac{dy}{dx} ). |
| A. | y=cx+ ( frac{1}{c+1} ) |
| B. | x=cy-(c+1) |
| C. | x=cy- ( frac{1}{c+1} ) |
| D. | y=cx+(c+1) |
| Answer» B. x=cy-(c+1) | |
| 5. |
Singular solution for the Clairaut s equation (y = y x+ frac{a}{y } ) is given by _______ |
| A. | ( frac{x^2}{a^2} + frac{y^2}{a^2} = 1 ) |
| B. | y<sup>2</sup>=-4ax |
| C. | y<sup>2</sup>=4ax |
| D. | x<sup>2</sup>=-2ay |
| Answer» D. x<sup>2</sup>=-2ay | |