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MHTCET 13 Apr 2026 Shift 1 Paper

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Question : 133 of 150

Marks: +1, -0

If

\frac{d y}{d x}=y+5

y(0)=4

y(\log 2)

is equal to

2
5
7
13

Solution:

Concept:

Solve the first-order differential equation by substitution, then use the initial condition to find the constant.

Explanation:

Let

z = y + 5

.

Then

\frac{dz}{dx} = \frac{dy}{dx}

.

The differential equation becomes

\frac{dz}{dx} = z

.

Its solution is

z = C e^{x}

.

Since

z = y+5

, we get

y+5 = C e^{x}

.

Using

y(0)=4

:

4+5 = C e^{0}

, so

C = 9

.

Therefore,

y = 9e^{x} - 5

.

Now substitute

x = \log 2

.

Since

e^{\log 2} = 2

, we have

y(\log 2) = 9(2) - 5 = 18 - 5 = 13

.

Answer:

y(\log 2) = 13

Option D.

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