Find the general solution of :
$\dfrac{{dy}}{{dx}} = 1 + x + y + xy$
Answer
381.6k+ views
Hint: Start by clubbing the terms, the next step is to take the common terms out, and then group the terms such that it is easier to integrate.
Complete step-by-step answer:
We have been given with a differential equation:
$\dfrac{{dy}}{{dx}} = 1 + x + y + xy$
Let us club the terms to simplify the process,
$\dfrac{{dy}}{{dx}} = \left( {1 + x} \right) + y\left( {1 + x} \right)$
Now take the common term out,
$\dfrac{{dy}}{{dx}} = \left( {1 + x} \right)\left( {1 + y} \right)$
Send the x terms on one side and the y terms to the other,
$\dfrac{{dy}}{{\left( {1 + y} \right)}} = \left( {1 + x} \right)dx$
On applying integration on both sides, we get,
$\int {\dfrac{{dy}}{{\left( {1 + y} \right)}}} = \int {\left( {1 + x} \right)dx} $
Answer = ${\log _e}|1 + y| = x + \dfrac{{{x^2}}}{2} + C$
Note: We started by arranging the terms such that it is easier to integrate and then integrated by using the formulas.
Complete step-by-step answer:
We have been given with a differential equation:
$\dfrac{{dy}}{{dx}} = 1 + x + y + xy$
Let us club the terms to simplify the process,
$\dfrac{{dy}}{{dx}} = \left( {1 + x} \right) + y\left( {1 + x} \right)$
Now take the common term out,
$\dfrac{{dy}}{{dx}} = \left( {1 + x} \right)\left( {1 + y} \right)$
Send the x terms on one side and the y terms to the other,
$\dfrac{{dy}}{{\left( {1 + y} \right)}} = \left( {1 + x} \right)dx$
On applying integration on both sides, we get,
$\int {\dfrac{{dy}}{{\left( {1 + y} \right)}}} = \int {\left( {1 + x} \right)dx} $
Answer = ${\log _e}|1 + y| = x + \dfrac{{{x^2}}}{2} + C$
Note: We started by arranging the terms such that it is easier to integrate and then integrated by using the formulas.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What are the measures one has to take to prevent contracting class 12 biology CBSE

Suggest some methods to assist infertile couples to class 12 biology CBSE

Amniocentesis for sex determination is banned in our class 12 biology CBSE

Trending doubts
The lightest gas is A nitrogen B helium C oxygen D class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Which place is known as the tea garden of India class 8 social science CBSE

What is pollution? How many types of pollution? Define it

Write a letter to the principal requesting him to grant class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a diagram of a plant cell and label at least eight class 11 biology CBSE
