 # decide if the given statement is true or false,and give a brief justiﬁcation for your answer.If true, you can quote a relevant deﬁnition or theorem. I a2linetagadaW 2020-11-09 Answered

decide if the given statement is true or false,and give a brief justiﬁcation for your answer.If true, you can quote a relevant deﬁnition or theorem. If false,provide an example,illustration,or brief explanation of why the statement is false.
Q) The system of differential equations $x\prime =ty+5\left(\mathrm{sin}t\right)y-3{e}^{t},y\prime ={t}^{2}x-7xy-1$ is a ﬁrst-order linear system of differential equations.

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Step 1
Given:
The system of differential equations ${x}^{\prime }=ty+5\left(\mathrm{sin}t\right)y-3{e}^{t},{y}^{\prime }={t}^{2}x-7xy-1$ is a first - order linear system of differential equations.
To decide:
The given statement is true or false.
Step 2
The given statement is true.
That is, the system of differential equations ${x}^{\prime }=ty+5\left(\mathrm{sin}t\right)y-{3}^{e}t,{y}^{\prime }={t}^{2}x-7xy-1$ is a first - order linear system of differential equations.
A linear equation or polynomial, with one or more terms, consisting of the derivatives of the dependent variable with respect to one or more independent variables is known as a linear differential equation.
The solution of the linear differential equation produces the value of the variable y.
Example:
$\frac{dy}{dx}+2y=\mathrm{sin}x$