1
COMEDK 2024 Evening Shift
+1
-0

The general solution of the differential equation $$x \frac{d y}{d x}=y+x \tan \left(\frac{y}{x}\right)$$ is

A
$$\sin \left(\frac{y}{x}\right)=\frac{C}{x}$$
B
$$\sin \left(\frac{y}{x}\right)=C x$$
C
$$\sin \left(\frac{x}{y}\right)=C x$$
D
$$\sin \left(\frac{x}{y}\right)=C y$$
2
COMEDK 2024 Evening Shift
+1
-0

$$\text { The general solution of the differential equation }(1+\tan y)(d x-d y)+2 x d y=0 \text { is }$$

A
$$y(\sin x+\cos x)=\sin x+c e^x$$
B
$$y(\sin x+\cos x)=\sin x+c e^{-x}$$
C
$$x(\sin y+\cos y)=\sin y+c e^y$$
D
$$x(\sin y+\cos y)=\sin y+c e^{-y}$$
3
COMEDK 2024 Evening Shift
+1
-0

The sum of the order and degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+\frac{4\left(\frac{d^2 y}{d x^2}\right)^3}{\left(\frac{d^3 y}{d x^3}\right)}+\frac{d^3 y}{d x^3}=x^2-1$$ is

A
4
B
5
C
6
D
8
4
COMEDK 2024 Evening Shift
+1
-0

$$\text { If } \frac{d y}{d x}=y+3>0 \text { and } y(0)=2 \text { then } y(\log 2) \text { is equal to }$$

A
5
B
13
C
$$-$$2
D
7
EXAM MAP
Medical
NEET