What is the solution to the equation 5x-2=2x+13?
1 answer:
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Answer:
Step-by-step explanation:
Let:
This is and exact equation, because:
So, define f(x,y) such that:
The solution will be given by:
Where C1 is an arbitrary constant
Integrate with respect to x in order to find f(x,y):
Where g(y) is an arbitrary function of y.
Differentiate f(x,y) with respect to y in order to find g(y):
Substitute into
Integrate with respect to y:
Substitute g(y) into f(x,y):
The solution is f(x,y)=C1
Solving y using quadratic formula:
Answer:
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Step-by-step explanation:
Using the fundamental theorem of calculus
Taking the derivative of the integral gives back the function
Since the lower limit is a constant when we take the derivative it is zero
d/dx
g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))
Replacing t with x
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))