diff --git a/src/differential_equations_1.md b/src/differential_equations_1.md
index c26190a1cda5a7282cb9b068de7ca855e3b66945..3246520725f12fce3e3266a8b6f820cf77597c10 100644
--- a/src/differential_equations_1.md
+++ b/src/differential_equations_1.md
@@ -774,14 +774,27 @@ since we have demonstrated that $**\phi**_{k}(t)$ is a solution of the DE.
 
 # Problems
 
-1.  [:grinning:]  Solve the equation $\dot{x}(t)=5x+3$ subject to the initial 
-        condition $x(0)=\frac{2}{5}$.
-
-2.  [:smirk:] Solve the equation $\dot{x}(t)=-tan(x)sin(x)$ subject to the initial 
-        condition $x(0)=1$. 
-
-3.  [:smirk:] Solve the equation $\dot{x(t)}=\frac{1}{3} x^2+9$ subject to the 
-        initial condition $x(0)=3$.
+1.  [:grinning:] Solve 
+        (a)  $\dot{x}(t) = t^5$
+        (b)  $\dot{x}(t) = cos(t)$
+
+2.  [:grinning:] Solve, subject to the initial condition $x(0)=\frac{1}{2}$
+        (a) $\dot{x}(t) = -x^3$
+        (b) $\dot{x}(t) = \lambda t x$
+        (c) $\dot{x}(t) = t x^{4}$
+
+3.  [:smirk:] Solve, subject to the given initial condition
+        (a) $\dot{x}(t)=-tan(x)sin(x)$, subject to $x(0)=1$. 
+        (b) $\dot{x(t)}=\frac{1}{3} x^2+9$, subject to $x(0)=3$.
+
+4. [:grinning:] Identify which of the following systems of equations is linear.
+        *Note thate you do not need to solve them!*  
+        (a) $$\dot{x_1}=t x_1 -3 x_2$$
+            $$\dot{x}_2 = x_1 x_2 - x_1$$
+        (b) $$\dot{x}_1 = e^{-t}x_1$$
+            $$\dot{x}_2 = \sqrt{t + cos(t)-4}x_1 + \frac{sin(t)}{t^2+t-1}x_2$$
+        (c) $$x^{(2)}_1 x_1 + \dot{x}_1 = 8 x_2$$
+            $$\dot{x}_2=5tx_2 + x_1$$