Methods of Solving First Order, First Degree Differential Equation

IMPORTANT

Methods of Solving First Order, First Degree Differential Equation: Overview

This Topic covers sub-topics such as First Order and First Degree Differential Equations, Variable Separable Form of Differential Equations, General Solution of Linear Differential Equation of First Order and, Homogeneous Form of Differential Equations

Important Questions on Methods of Solving First Order, First Degree Differential Equation

EASY
IMPORTANT

Solve the following differential equation dydx=1+x21+y2

MEDIUM
IMPORTANT

Solve the differential equation dydx=- x+ycosx1+sin x. 

MEDIUM
IMPORTANT

Solve the differential equation, x(x+y)dy=(x2+y2)dx.

MEDIUM
IMPORTANT

Find a particular solution of the differential equation given below

(tan1yx)dy=(1+y2)dx given that y=0 when x=0.

MEDIUM
IMPORTANT

Solve the differential equation

xdydx+y=x2y4

MEDIUM
IMPORTANT

Find the general solution of the differential equation xdydx+2y=x2 x0.

HARD
IMPORTANT

Solution of the differential equation dydx=sec2x+2xe-x+tanx2yey2-x is ?

HARD
IMPORTANT

Following are the differential equations and their respective solutions. Select the incorrect one.

I y'=asin2x-sinx: y=asin2x+cosx+9

II y'=b2xlogx: y=blogx+2

III y'=-7x+3sec23x+5excos5x+exsin5x: y=-7+exsin5x+tan3x

EASY
IMPORTANT

If area of triangle formed by tangent (with positive slope) and normal to a curve at any point in first quadrant with x-axis is cube of its ordinate,then differential equation of such family is:

 

EASY
IMPORTANT

The general solution of the differential equation y'=4xx-4   is?

MEDIUM
IMPORTANT

Find the particular solution of the differential equation logdydx=3x+4y given that y=0 when x=0.

MEDIUM
IMPORTANT

Find the equation of a curve passing through the point 0, 1. If the slope of the tangent to the curve at any point x, y is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

MEDIUM
IMPORTANT

Find the general solution of the differential equation y dx-x+2y2dy=0.

MEDIUM
IMPORTANT

Show that the family of curves for which the slope of the tangent at any point x, y on it is x2+y22xy, is given by x2-y2=cx.

MEDIUM
IMPORTANT

Show that the differential equation 2y exydx+y-2x exydy=0 is homogeneous and find its particular solution, given that, x=0 when y=1.

MEDIUM
IMPORTANT

Show that the differential equation x cosyxdydx=y cosyx+x is homogeneous and solve it.