Explore topic-wise MCQs in Ordinary Differential Equations.

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.

What is the solution of D.E (D2 2D)y = ex sin x when solved using the method of undetermined coefficients?

A. ( y = c_1 + c_2 ,e^{2x} frac{e^x (xsin x + cos u2061x)}{2} )
B. (y = c_1 + c_2 ,e^{2x} frac{e^x sin x}{2} )
C. (y = c_1 + c_2 ,e^{2x} frac{e^x cos x}{2} )
D. (y = c_1 + c_2 ,e^{2x} frac{e^x (sin x + x cos u2061x)}{4} )
Answer» C. (y = c_1 + c_2 ,e^{2x} frac{e^x cos x}{2} )
Discussion
2.

Using the method of undetermined coefficients find the P.I for the D.E x (t) x (t) = 3et + sin t.

A. x<sub>p</sub> = 3e<sup>t</sup> + ( frac{t}{2} ) (cos u2061t 2 sin u2061t )
B. x<sub>p</sub> = 3te<sup>t</sup> + ( frac{1}{2} ) (cos u2061t + sin u2061t )
C. x<sub>p</sub> = 3te<sup>t</sup> + ( frac{t}{3} ) (4cos u2061t + 2sin u2061t )
D. x<sub>p</sub> = 3e<sup>t</sup> + ( frac{1}{2} ) (cos u2061t sin u2061t )
Answer» C. x<sub>p</sub> = 3te<sup>t</sup> + ( frac{t}{3} ) (4cos u2061t + 2sin u2061t )
Discussion
3.

Find the Particular integral solution of the D.E (D2 4D + 3)y = 20 cos x by the method of undetermined coefficients.

A. y<sub>p</sub> = 4 cos u2061x 3 sin u2061x
B. y<sub>p</sub> = 2 sin u2061x 4 cos u2061x
C. y<sub>p</sub> = 3 cos u2061x + 4 sin u2061x
D. y<sub>p</sub> = 2 cos u2061x 4 sin u2061x
Answer» E.
Discussion
4.

Solution of the D.E y + 3y + 2y = 12x2 when solved using the method of undetermined coefficients is ________

A. y = c<sub>1</sub> e<sup>x</sup> + c<sub>2</sub> e<sup>2x</sup> + 2 11x + x<sup>2</sup>
B. y = c<sub>1</sub> e<sup> x</sup> + c<sub>2</sub> e<sup> 2x</sup> + 18 + 21x + 3x<sup>2</sup>
C. y = c<sub>1</sub> e<sup>x</sup> + c<sub>2</sub> e<sup> 2x</sup> + 11 + 18x + 2x<sup>2</sup>
D. y = c<sub>1</sub> e<sup> x</sup> + c<sub>2</sub> e<sup> 2x</sup> + 21 18x + 6x<sup>2</sup>
Answer» E.
Discussion
5.

Solution of the D.E y 4y + 4y = ex when solved using method of undetermined coefficients is _____

A. y = (c<sub>1</sub> + c<sub>2</sub>)e<sup>2x</sup> + 2e<sup>x</sup> 1
B. y = (c<sub>1</sub> + c<sub>2</sub> x)e<sup>2x</sup> + 4e<sup>x</sup> 4
C. y = (c<sub>1</sub> + c<sub>2</sub> x)e<sup>2x</sup> + e<sup>x</sup>
D. y = (c<sub>1</sub> + c<sub>2</sub> x)e<sup>x</sup> + 4e<sup>x</sup>
Answer» D. y = (c<sub>1</sub> + c<sub>2</sub> x)e<sup>x</sup> + 4e<sup>x</sup>
Discussion