Aditya tried to solve the differential equation (dy)/(dx)=6x-30. This is his work: (dy)/(dx)=6x-30 Step 1: quad int30 dy=int6xdx Step 2: quad30 y=3x^(2)+C Step 3: quad y=(x^(2))/(10)+C Is Aditya's work correct? If not, what is his mistake? Choose 1 answer: (A) Aditya's work is correct. (B) Step 1 is incorrect. The separation of variables wasn't done correctly. (C) Step 2 is incorrect. Aditya didn't integrate 30 correctly. (D) Step 3 is incorrect. The right-hand side of the equation should be (30)/(3x^(2)+C).

Separate variables: Aditya is given the differential equation (dy)/(dx) = 6x - 30 and attempts to solve it by separating variables and integrating both sides. Let's check his work step by step. Step 1: Separate variables. (dy)/(dx) = 6x - 30 ∫dy = ∫(6x - 30)dx This is the correct method for separating variables.Integrate both sides: Integrate both sides. ∫dy = ∫(6x - 30)dx 30y = 3x^2 - 30x + C Aditya integrated the right side correctly, but he forgot to integrate the -30x term.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Aditya tried to solve the differential equation
(dy)/(dx)=6x-30. This is his work:

(dy)/(dx)=6x-30
Step 1:
quad int30 dy=int6xdx
Step 2:
quad30 y=3x^(2)+C
Step 3:
quad y=(x^(2))/(10)+C
Is Aditya's work correct? If not, what is his mistake?
Choose 1 answer:
(A) Aditya's work is correct.
(B) Step 1 is incorrect. The separation of variables wasn't done correctly.
(C) Step 2 is incorrect. Aditya didn't integrate 30 correctly.
(D) Step 3 is incorrect. The right-hand side of the equation should be
(30)/(3x^(2)+C).

Aditya tried to solve the differential equation $\frac{d y}{d x}=6 x-30$ . This is his work: $\newline$ $\frac{d y}{d x}=6 x-30$ $\newline$ Step $1$ : $\quad \int 30 d y=\int 6 x d x$ $\newline$ Step $2$ : $\quad 30 y=3 x^{2}+C$ $\newline$ Step $3$ : $\quad y=\frac{x^{2}}{10}+C$ $\newline$ Is Aditya's work correct? If not, what is his mistake? $\newline$ Choose $1$ answer: $\newline$ (A) Aditya's work is correct. $\newline$ (B) Step $1$ is incorrect. The separation of variables wasn't done correctly. $\newline$ (C) Step $2$ is incorrect. Aditya didn't integrate $30$ correctly. $\newline$ (D) Step $3$ is incorrect. The right-hand side of the equation should be $\frac{30}{3 x^{2}+C}$ .

View step-by-step help

Home

Math Problems

Algebra 1

Transformations of functions

Full solution

Q. Aditya tried to solve the differential equation

\frac{d y}{d x}=6 x-30

. This is his work:

\newline

\frac{d y}{d x}=6 x-30

\newline

Step

1

\quad \int 30 d y=\int 6 x d x

\newline

Step

2

\quad 30 y=3 x^{2}+C

\newline

Step

3

\quad y=\frac{x^{2}}{10}+C

\newline

Is Aditya's work correct? If not, what is his mistake?

\newline

Choose

1

answer:

\newline

(A) Aditya's work is correct.

\newline

(B) Step

1

is incorrect. The separation of variables wasn't done correctly.

\newline

2

is incorrect. Aditya didn't integrate

30

correctly.

\newline

(D) Step

3

is incorrect. The right-hand side of the equation should be

\frac{30}{3 x^{2}+C}

Separate variables: Aditya is given the differential equation $(\frac{dy}{dx} = 6x - 30)$ and attempts to solve it by separating variables and integrating both sides. $\newline$ Let's check his work step by step. $\newline$ Step $1$ : Separate variables. $\newline$ $(\frac{dy}{dx} = 6x - 30)$ $\newline$ $\int dy = \int (6x - 30)dx$ $\newline$ This is the correct method for separating variables.
Integrate both sides: Integrate both sides. $\newline$ $\int dy = \int (6x - 30)dx$ $\newline$ $30y = 3x^2 - 30x + C$ $\newline$ Aditya integrated the right side correctly, but he forgot to integrate the $-30x$ term.