1
MHT CET 2023 9th May Morning Shift
+2
-0

The particular solution of the differential equation $$\left(1+y^2\right) \mathrm{d} x-x y \mathrm{~d} y=0$$ at $$x=1, y=0$$, represents

A
circle
B
pair of straight lines
C
hyperbola
D
ellipse
2
MHT CET 2021 21th September Evening Shift
+2
-0

$$\text{I} : y^{\prime}=\frac{y+x}{x} ; \quad \text { II }: y^{\prime}=\frac{x^2+y}{x^3} ; \quad \text { III }: y^{\prime}=\frac{2 x y}{y^2-x^2}$$

S1 : Differential equations given by I and II are homogeneous differential equations.

S2 : Differential equations given by II and III are homogeneous differential equations.

S3 : Differential equations given by I and III are homogeneous differential equations.

A
only S1 is valid
B
both S1 and S2 are valid
C
only S3 is valid
D
only S2 is valid.
3
MHT CET 2021 21th September Evening Shift
+2
-0

The differential equation of the family of circles touching $$y$$-axis at the origin is

A
$$x^2-y^2-2 x y \frac{d y}{d x}=0$$
B
$$x^2-y^2+2 x y \frac{d y}{d x}=0$$
C
$$x^2+y^2-2 x y \frac{d y}{d x}=0$$
D
$$x^2+y^2+2 x y \frac{d y}{d x}=0$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

The general solution of the differential equation. $$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\left(\frac{x}{y}\right) \sin \left(\frac{y}{x}\right)+\cos \left(\frac{y}{x}\right)\right] d y=0$$ is

A
$$y^2 \sin \left(\frac{y}{x}\right)=k$$
B
$$\mathrm{x} \sin \left(\frac{\mathrm{y}}{\mathrm{x}}\right)=\mathrm{k}$$
C
$$\sin \left(\frac{y}{x}\right)=k$$
D
$$y \sin \left(\frac{y}{x}\right)=k$$
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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