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Which of the following functions is a solution for the differential equation dy/dx -14x = 0?
- a)y = 7x2
- b)y = 7x3
- c)y = x7
- d)y = 14x
Correct answer is option 'A'. Can you explain this answer?
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Which of the following functions is a solution for the differential eq...
Consider the function y = 7x2
Differentiating w.r.t x, we get
dy/dx -14x
⇒ dy/dx -14x = 0
Hence, the function y = 7x2 is a solution for the differential equation dydx - 14x = 0
Differentiating w.r.t x, we get
dy/dx -14x
⇒ dy/dx -14x = 0
Hence, the function y = 7x2 is a solution for the differential equation dydx - 14x = 0
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Which of the following functions is a solution for the differential eq...
Given: dy/dx -14x = 0
To find the solution for the given differential equation, we need to find a function y(x) that satisfies the equation.
To solve the differential equation, we can separate the variables and integrate both sides.
Separating the variables:
dy = 14x dx
Integrating both sides:
∫dy = ∫14x dx
Using the power rule of integration, we can integrate both sides:
y = 7x^2 + C
where C is the constant of integration.
Now, we have the general solution to the differential equation: y = 7x^2 + C.
To determine the specific solution, we need an initial condition or boundary condition. Since no initial condition is given in the question, we cannot determine the value of C.
Therefore, the solution to the differential equation dy/dx -14x = 0 is y = 7x^2 + C, where C is a constant.
Among the given options, option A (y = 7x^2) is the only function that satisfies the differential equation dy/dx -14x = 0, as it is the general solution without the constant of integration.
To find the solution for the given differential equation, we need to find a function y(x) that satisfies the equation.
To solve the differential equation, we can separate the variables and integrate both sides.
Separating the variables:
dy = 14x dx
Integrating both sides:
∫dy = ∫14x dx
Using the power rule of integration, we can integrate both sides:
y = 7x^2 + C
where C is the constant of integration.
Now, we have the general solution to the differential equation: y = 7x^2 + C.
To determine the specific solution, we need an initial condition or boundary condition. Since no initial condition is given in the question, we cannot determine the value of C.
Therefore, the solution to the differential equation dy/dx -14x = 0 is y = 7x^2 + C, where C is a constant.
Among the given options, option A (y = 7x^2) is the only function that satisfies the differential equation dy/dx -14x = 0, as it is the general solution without the constant of integration.
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Which of the following functions is a solution for the differential equationdy/dx -14x = 0?a)y = 7x2b)y = 7x3c)y = x7d)y = 14xCorrect answer is option 'A'. Can you explain this answer?
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