1
KCET 2023
MCQ (Single Correct Answer)
+1
-0

The degree of the differential equation $$1+\left(\frac{d y}{d x}\right)^2+\left(\frac{d^2 y}{d x^2}\right)^2=\sqrt[3]{\frac{d^2 y}{d x^2}+1}$$ is

A
3
B
1
C
2
D
6
2
KCET 2022
MCQ (Single Correct Answer)
+1
-0

If $$\frac{d y}{d x}+\frac{y}{x}=x^2$$, then $$2 y(2)-y(1)=$$

A
$$\frac{11}{4}$$
B
$$\frac{15}{4}$$
C
$$\frac{9}{4}$$
D
$$\frac{13}{4}$$
3
KCET 2022
MCQ (Single Correct Answer)
+1
-0

The solution of the differential equation $$\frac{d y}{d x}=(x+y)^2$$ is

A
$$\tan ^{-1}(x+y)=x+C$$
B
$$\tan ^{-1}(x+y)=0$$
C
$$\cot ^{-1}(x+y)=C$$
D
$$\cot ^{-1}(x+y)=x+C$$
4
KCET 2022
MCQ (Single Correct Answer)
+1
-0

If $$y(x)$$ is the solution of differential equation $$x \log x \frac{d y}{d x}+y=2 x \log x, y(e)$$ is equal to

A
e
B
0
C
2
D
2e
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