Solve the differential equation: from Mathematics Differential

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

Advertisement

151.

Solve the differential equation:
dy over dx space equals space straight y space sin space 2 straight x comma space space space given space that space space straight y left parenthesis 0 right parenthesis space equals space 1.


The given differential equation is
                           dy over dx space equals space straight y space sin space 2 straight x
Separating the variables, we get,
                    1 over straight y dy space equals space sin space 2 straight x space dx
Integrating,  integral 1 over straight y dy space equals space integral sin space 2 straight x space dx
therefore space space space log space open vertical bar straight y close vertical bar space equals space minus fraction numerator cos space 2 straight x over denominator 2 end fraction plus straight c                          ...(1)
Now     straight y left parenthesis 0 right parenthesis space equals space 1 space space space space space space space space space space space space rightwards double arrow space space space straight y space equals space 1 space space space space when space straight x space equals space 0
therefore space space log space open vertical bar 1 close vertical bar space equals space minus fraction numerator cos space 0 over denominator 2 end fraction plus straight c space space space space space rightwards double arrow space space 0 space equals space minus 1 half plus straight c space space space space rightwards double arrow space space space space straight c space equals space 1 half
therefore space space from space left parenthesis 1 right parenthesis space space space log space open vertical bar straight y close vertical bar space equals space minus 1 half space cos space 2 straight x space plus 1 half space which space is space required space solution. space
87 Views

Advertisement
152.

Solve the following initial value problem:
(1 + x y) y dx + (1 – x y) x dy = 0, y (1) = 1.

114 Views

153. Find the particular solution of the differential equation dy over dx space equals space minus 4 xy squared given that y = 1,  when x = 0.

88 Views

154. Find the particular solution of the differential equation
(1 + e2x ) dy + (1 + y2 ) ex dx = 0, given that y = 1 when x = 0.
91 Views

Advertisement
155. Find the solution of the equation:
            dy over dx space equals space straight e to the power of straight x plus straight y end exponent plus straight x squared space straight e to the power of straight x
subject to the condition, when x = 0;  y = 0.
88 Views

156.

Solve the differential equation;
x (1 + y2 ) dx – y (1 + x2 ) dy = 0  given that y = 0 when x = 1. 

84 Views

 Multiple Choice QuestionsLong Answer Type

157. Find the particular solution of (1 + x2 + y2 + x2 y2 ) dx + x y dy = 0
87 Views

 Multiple Choice QuestionsShort Answer Type

158. Find the particular solution of the differential equation log space open parentheses dy over dx close parentheses space equals space 3 straight x plus 4 straight y given that y = 0 when x = 0.
77 Views

Advertisement
159.

Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2 x2 + 1) dx (x ≠ 0).

78 Views

 Multiple Choice QuestionsLong Answer Type

160. Find the equation of a curve passing through the point (– 2, 3), given that the slope of the tangent to the curve at any point (x, y) is fraction numerator 2 straight y over denominator straight y squared end fraction.
82 Views

Advertisement